Wheel balance, also frequently referred to as wheel imbalance, wheel unbalance, tire balance, tire imbalance or tire unbalance, relates to the distribution of mass within a vehicle tire and the wheel to which it is attached. Herein, the vehicle tire and the wheel to which it is attached, including the stem and stem pressure sensor, if so equipped, are referred to as the “wheel assembly”. When the wheel assembly rotates, a non-uniform distribution of mass about the spin axis can cause the wheel assembly to produce periodic forces and moments at the frequency of the rotation rate of the wheel. These forces and moments can give rise to ride disturbances, usually vertical and fore-aft vibrations and can be considered objectionable by the occupants of the vehicle. Furthermore, the forces and moments produced by these non-uniformities in mass distribution originate in inertial mechanisms, resulting in a monotonic increase in amplitudes with speed. In addition, vehicle suspensions can be disproportionately excited by the unbalanced forces when the speed of the wheel assembly reaches a point that its rotating frequency coincides with a suspension's resonant frequency producing elevated disturbances detectable by occupants. The potential occurrence of these perceptible disturbances arising from imbalance excitation in isolation or in combination with other internally generated force and moment excitation at the spindles of the vehicle, created by common operation of the vehicle at usage speeds, demands attention. Tires are therefore inspected for balance in tire factories; wheel assemblies are inspected at vehicle assembly plants and repair shops by one of two methods: static balancing and dynamic balancing. Tires with excessive imbalance are reworked, downgraded or rejected. When tires are fitted to wheels to produce a wheel assembly at vehicle assembly plants, subassembly operations prior to delivery to vehicle assembly plants, or the point of sale at retail shops, the wheel assembly is measured for balance and correction weights are most typically applied to the wheel of the wheel assembly to counteract the imbalance.
Static balance can be measured by a static balancing machine where the wheel assembly is typically placed horizontally on a non-rotating spindle tool with freedom to angulate about a pivot on the intended, vertically oriented spin axis. The mass distribution is acted on by gravity, and the location on the wheel assembly where the integrated effect of the mass distribution is greatest causes the spindle tool to deflect downward at that point. The amount of deflection indicates the magnitude of the effective imbalance. The angle of the deflection indicates the angular location of the effective imbalance. In tire manufacturing factories, static balancers operate by use of sensors mounted to the spindle assembly. In tire retail shops, static balancers are usually non-rotating bubble balancers, where the magnitude and angle of the wheel assembly imbalance is indicated by the position of the center bubble in an oil-filled glass sighting gauge.
Dynamic balance describes the forces generated by particular uneven mass distributions when the wheel assembly is rotated, usually at a relatively high speed. Dynamic balance is more comprehensive than static balance alone, because both dynamic forces and moments of the wheel assembly are measured and attempted to be corrected. These dynamic machines typically sense multiple reaction forces of a stiff spindle as the tire rotates at sufficient speed to enable sensing of the inertially created forces. In the tire manufacturing factory, the tire is mounted on a balancing machine test wheel, the assembly is accelerated to a speed of 300 RPM or higher, and sensors measure the multiple forces of imbalance as the tire rotates. These forces are ultimately resolved into equivalent static and couple (i.e., moment or torque) values, using techniques well know in the art. These forces and moments are further transformed into equivalent imbalance amounts at the inner and outer planes of the wheel, and compared to the imbalance tolerances (the maximum allowable manufacturing limits). The methodologies and processes have evolved over the years to address the determination of an effective centroid of mass within the envelope of the tire and wheel assembly whose location is not on the spin axis. These can be mathematically conceptualized as applications of the first integrals of mass for determination of the first order contributions of the mass distributions to periodic inertial force systems occurring at the spindles. Although other harmonics of mass distribution can become significant owing to the deformable tire, and thereby, produce perceptible disturbance levels, those associated with the first moments of mass account for a disproportionately large percentage of vibration complaints.
In tire retail shops, wheel assemblies are checked on a dynamic spin-balancer, which determines two corrective balance weights and respective corresponding angles for each corrective balance weight, with respect to an angle reference determined by the spin-balancer, at which each corrective balance weight is to be placed at a predetermined radius at each of two separate predetermined planes to attempt to minimize the couple and static forces and also minimize the couple and static balance residuals so as to correct for static and dynamic wheel assembly imbalance within a predetermined limit for couple residual of the wheel assembly as determined by the spin-balancer.
In manufacturing and assembly plants, the two separate planes and the radius for affixing the corrective balance weights of each of the two separate planes are predetermined by the design of the wheel assembly. For example, a first predetermined plane may be that which is perpendicular to the axis of rotation of the wheel assembly at the outer flange of the wheel and the predetermined radius in the first plane may be that from the axis of rotation of the wheel assembly to the rim of the outer flange of the wheel; whereas a second predetermined plane may be that which is perpendicular to the axis of rotation of the wheel assembly and at the inner flange of the wheel, and the predetermined radius in the second plane may be that from the axis of rotation of the wheel assembly to the rim of the inner flange of the wheel.
However, corrective balance weights usually have discrete values defined by a predetermined minimum incremental weight, for example the predetermined minimum incremental weight may be ¼ oz, resulting in available adjacent discrete corrective balance weights varying by ¼ oz increments. As such, the two required, precise balance weights (one balance weight for each plane) determined by the spin-balancer may not be available. In one current practice, the two precise balance weights determined by the spin-balancer are each rounded to the nearest available corrective balance weight to produce two “best” selected corrective balance weights. This method is herein referred to as the “rounding” method. The two selected available corrective balance weights, if different from the two precise balance weights determined by the spin-balancer, as is usually the case, cannot simultaneously satisfy static and, or couple balance of the wheel assembly if placed at the respective corresponding angles for the two precise balance weights determined by the spin-balancer.
Further elaborating the common prior art practice, the rounding method involves recalculating the angles for each selected corrective balance weight to be placed at each predetermined radius of each of the two separate predetermined planes in order to attempt to best correct static imbalance forces of the wheel assembly as determined by the spin-balancer by minimizing the residual for static balance within a predetermined limit for couple residual. The techniques for determining and calculating couple and static forces and couple and static residuals to correct static imbalance forces of the wheel assembly within a predetermined limit for couple residual of the rounding method are well know to the practitioners of the art. In many cases, however, this common practice is unsatisfactory, leaving high static and, or couple residuals.
FIG. 1 depicts a wheel assembly 102 having an axis of rotation 104 (i.e., the vehicle wheel axle), tire 106, wheel 108, a second axis 110, and a third axis 112. As a first example of the prior art method of wheel balancing and using the rounding method, the wheel assembly 102 has a total equivalent static imbalance of 2.24 oz as determined by a spin-balancer, represented in FIG. 2, viewed along the third axis 112, of a first precise imbalance weight 114 of 1.12 oz occurring at a first predetermined radius 116 in a first predetermined plane 118 and a second precise imbalance weight 120 of 1.12 oz occurring at a second predetermined radius 122 in a second predetermined plane 124, axially displaced along the direction of the spin axis from that of the first predetermined plane. With the constrained placement of correction weights within the two predetermined planes 118 and 124, the wheel assembly 102 requires two equal corrective balance weights of 1.12 oz placed at points 126 and 128 with radii 130 and 132, respectively, as determined by a spin-balancer in order to balance the wheel assembly wherein radii 116, 122, 130, and 132 are equal. FIG. 3, viewed along the second axis 110, depicts the location of the two 1.12 oz precise imbalance weights 114 and 120 as well as points 126 and 128.
Assuming availability of corrective balance weights only in increments of ¼ oz, the closest corrective balance weight obtainable to 1.12 oz is a 1 oz selected corrective balance weight. FIG. 4, viewed along the third axis 112, depicts the two 1 oz selected corrective balance weights 134 and 136 placed at points 126 and 128, respectively. In conjunction with the two 1.12 oz precise imbalance weights 114 and 120, the two 1 oz selected corrective balance weights 134 and 136 placed at points 126 and 128 do not produce any couple residual imbalance but do produce a static residual imbalance of 0.24 oz of the wheel assembly 102, due to the use of available discrete selected corrective balance weights, discrete balance weight increments and the rounding method. The techniques used for determining the couple and static residual imbalance of the wheel assembly 102 within a predetermined limit for couple residual are well know to the practitioners of the art.
As a second example of the prior art method of wheel balancing, the wheel assembly 102 has a total static precise imbalance of 3.75+ oz as determined by a spin-balancer, equivalently represented in FIG. 5, viewed along the third axis 112, of a first precise imbalance weight 114′ of 1.875+ oz occurring at a first predetermined radius 116 of a first predetermined plane 118 and a second precise imbalance weight 120′ of 1.875+ oz occurring at a second predetermined radius 122 of a second predetermined plane 124. (The ‘+’ suffix following the numbers signifies an extremely small, non-zero increment over the value of the number.) With the constrained placement of corrective weights within the two predetermined planes 118 and 124, the wheel assembly 102 requires two equal corrective balance weights of 1.875+ oz placed at points 126 and 128 with radii 130 and 132, respectively, as determined by a spin-balancer, to balance the wheel assembly, wherein radii 116, 122, 130, and 132 are equal. FIG. 6 viewed along the second axis 110 depicts the location of the two 1.875+ oz precise imbalance weights 114′ and 120′ as well as points 126 and 128.
Assuming the availability of corrective balance weights only in increments of ¼ oz and a predetermined limit for couple residual of 0.25 oz, the following situation arises in attempting to balance the assembly. The closest corrective balance weight obtainable to 1.875+ oz is a 2 oz selected corrective balance weight. As determined by a spin-balancer and applying the rounding method, the wheel assembly 102 requires two equal selected corrective balance weights of 2 oz placed at points 126′ and 128′ with projections of radii 130′ and 132′ respectively, at an angle α=7.2 degrees, 150, on the first predetermined plane 118 and α′=7.2 degrees, 152, on the second predetermined plane 124, as depicted in FIGS. 7 and 8, to balance the wheel assembly, wherein projections of radii 130′ and 132′ are equal and radii 116 and 122 are equal.
FIG. 8, viewed along the third axis 112, depicts the two 2 oz selected corrective balance weights 138 and 140 placed at points 126′ and 128′, respectively. In conjunction with the two 1.875+ oz precise imbalance weights 114′ and 120′, the two 2 oz selected corrective balance weights 138 and 140 placed at points 126′ and 128′ produce a couple residual imbalance of 0.25 oz and a static residual imbalance of 0.22 oz of the wheel assembly 102 due to the use of discrete selected corrective balance weights, discrete balance weight increments and the rounding method, determined by techniques well know to practitioners of the art.
FIG. 9, viewed along the second axis 110, depicts the hypothetical location of the two 1.875+ oz 114′ and 120′ precise imbalance weights and the actual placement of the two 2 oz selected corrective balance weights 138 and 140 placed at points 126′ and 128′ having projections of radii 142 and 144, respectively, wherein projections of radii 142 and 144 are equal.
It will be shown in subsequent sections by contrasting the specific examples set forth in the preceding that the prior art rounding method is limited due to the resulting residuals in attempting to minimize the couple and static forces and couple and static balance residuals to correct for static and dynamic wheel assembly imbalance within a predetermined limit for couple residual.
Accordingly, what is needed in the art is a method to minimize the couple and static forces and couple and static balance residuals to correct for static and dynamic wheel assembly imbalance within a predetermined limit for couple residual with respect to the prior art method using discrete balance weights and discrete balance weight increments.